I hope so. I have 2" multifiliment woven nylon mesh netting over the top secured at the edges to the fence. It isn't terribly heavy, but it is strong and fairly hard to cut with scissors. I ran a nylon rope around the edges and zip tied them to the top bar of the chain link fence. It won't keep out raccoons or opposums, but the girls are locked in during the dark hours. Hawks are the primary daytime threat in our area.
On a side note, the mesh must warn them off. A large red-tail was floating along the fence line over the weekend "surveying the buffet" as my DH said. He moved on and didn't come back. I guess the mice in the pasture were an easier prey.